[gaming_mouse]

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now how do you incorporate the house edge into this argument? ... Would you first calculate the simple expected end amount of playing out the wagering requirement as

E_end_amount = (B+D) - WR*HA

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No. An important point for analyzing bonuses is that busting out relieves you of the wagering requirement. You also have to worry about completing the wagering requirement while you are not close to busting out or reaching your target.

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So how would you determine your chance of winning in these cases?

To take a concrete example, consider a 50% sticky bonus on $1000 which requires a 35*(D+B) WR (a total of $52,500). The best available game to complete this bonus is European Blackjack, with a house edge of .55% (so the house expects to get back $289). Given a target of, say, $2000, what is the chance that you win?

And how would the concern of completing the WR somewhere in between busting out and hitting your target come into play? What can you do about this concern?

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I think a better strategy is to aim for T+WR'*HA, where WR' is the remaining wagering requirement after betting. Either bet everything, or bet just what you need to reach T+WR'*HA. Once you reach T+WR'*HA, grind out the wagering requirement with tiny bets.

I believe my strategy decreases the average amount wagered, hence increases the probability of success. The exact performance is messy, but should be easy to test by experiment.

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This makes sense.